Related papers: Principal ideals in a plactic monoid always inters…

Our first main result shows that a graph product of right cancellative monoids is itself right cancellative. If each of the component monoids satisfies the condition that the intersection of two principal left ideals is either principal or…

The purpose of this note is to study some algebraic properties of irreducible ideals of monoids. We establish relations between irreducible, prime, and semiprime ideals. We explore some properties of irreducible ideals in local, Noetherian,…

We give a thorough structural analysis of the principal one-sided ideals of arbitrary semigroups, and then apply this to full transformation semigroups and symmetric inverse monoids. One-sided ideals of these semigroups naturally occur as…

We characterize monomial ideals which are intersections of monomial prime ideals and study classes of ideals with this property, among them polymatroidal ideals.

In this paper, basic properties of monomial difference ideals are studied. We prove the finitely generated property of well-mixed difference ideals generated by monomials. Furthermore, a finite prime decomposition of radical well-mixed…

This paper proves that a plactic monoid of any finite rank will have decidable first order theory. This resolves other open decidability problems about the finite rank plactic monoids, such as the Diophantine problem and identity checking.…

We consider the general question of how the homological finiteness property left-FPn holding in a monoid influences, and conversely depends on, the property holding in the substructures of that monoid. In particular we show that left-FPn is…

For the family of graded lattice ideals of dimension 1, we establish a complete intersection criterion in algebraic and geometric terms. In positive characteristic, it is shown that all ideals of this family are binomial set theoretic…

It is well-known that if R is a domain with finite character, each locally principal nonzero ideal of R is invertible. We address the problem of understanding when the converse is true and survey some recent results.

This paper presents new results on the identities satisfied by the hypoplactic monoid. We show how to embed the hypoplactic monoid of any rank strictly greater than 2 (including infinite rank) into a direct product of copies of the…

We exhibit a faithful representation of the plactic monoid of every finite rank as a monoid of upper triangular matrices over the tropical semiring. This answers a question first posed by Izhakian and subsequently studied by several…

If $I$ is a monomial ideal with linear quotients, then it has componentwise linear quotients. However, the converse of this statement is an open question. In this paper, we provide two classes of ideals for which the converse of this…

It is shown that plactic monoids satisfy nontrivial identities.

We classify all convex polyomino ideals which are linearly related or have a linear resolution. Convex stack polyominoes whose ideals are extremal Gorenstein are also classified. In addition, we characterize, in combinatorial terms, the…

The main result of this paper is that all antichains are finite in the poset of monomial ideals in a polynomial ring, ordered by inclusion. We present several corollaries of this result, both simpler proofs of results already in the…

Building on coprincipal mesoprimary decomposition [Kahle and Miller, 2014], we combinatorially construct an irreducible decomposition of any given binomial ideal. In a parallel manner, for congruences in commutative monoids we construct…

An ideal of polynomials is symmetric if it is closed under permutations of variables. We relate general symmetric ideals to the so called Specht ideals generated by all Specht polynomials of a given shape. We show a connection between the…

Interpolation theory for complex polynomials is well understood. In the non-commutative quaternionic setting, the polynomials can be evaluated "on the left" and "on the right". If the interpolation problem involves interpolation conditions…

In this paper we prove that the gradient ideal of a Morse polynomial is radical. This gives a generic class of polynomials whose gradient ideals are radical. As a consequence we reclaim a previous result that the unconstrained polynomial…

This work is dedicated to the results were got in the model theory of the regular polygons. We give the characterization of the monoids with axiomatizable and model complete class of regular polygons. We describe the monoids with complete…